Energy systems (e.g. ventilation fans, refrigerators, and electrical vehicle chargers) often have binary or discrete states due to hardware limitations and efficiency characteristics. Typically, such systems have additional programmatic constraints, such as minimum dwell times to prevent short cycling. As a result, non-convex techniques, like dynamic programming, are generally required for optimization. Recognizing developments in the field of distributed convex optimization and the potential for energy systems to participate in ancillary power system services, it is advantageous to develop convex techniques for the approximate optimization of energy systems. In this manuscript, we develop the alternative control trajectory representation — a novel approach for representing the control of a non-convex discrete system as a convex program. The resulting convex program provides a solution that can be interpreted stochastically for implementation.

Although China’s high-speed railway (HSR) is maturing after more than ten years of construction and development, the load factor and revenue of HSR could still be improved by optimizing the ticket fare structure. Different from the present unitary and changeless fare structure, this paper explores the application of multigrade fares to China’s HSR. On the premise that only one fare grade can be offered for each origin-destination (O-D) at the same time, this paper addresses the questions of how to adjust ticket price over time to maximize the revenue. First, on the basis of piecewise pricing strategy, a ticket fare optimization model is built, which could be transformed to convex program to be solved. Then, based on the analysis of passenger arrival regularity using historical ticket data of Beijing-Shanghai HSR line, several experiments are performed using the method proposed in the paper to explore the properties of the optimal multigrade fare scheme.

This paper is devoted to the study of solving method for a type of inverse linear semidefinite programming problem in which both the objective parameter and the right-hand side parameter of the linear semidefinite programs are required to adjust. Since such kind of inverse problem is equivalent to a mathematical program with semidefinite cone complementarity constraints which is a rather difficult problem, we reformulate it as a nonconvex semi-definte programming problem by introducing a nonsmooth partial penalty function to penalize the complementarity constraint. The penalized problem is actually a nonsmooth DC programming problem which can be solved by a sequential convex program approach. Convergence analysis of the penalty models and the sequential convex program approach are shown. Numerical results are reported to demonstrate the efficiency of our approach.

One of the numerically preferred methods for fitting a function to noisy data when the underlying function is known to be smooth is to minimize the roughness of the fit while placing a limit on the sum of squared errors. We show that the fit can be formulated as a solution to a convex program. Since convex programs can be solved by various methods with guaranteed convergence, our formulation enables one to use these methods to compute the fit numerically. Numerical results show that our formulation is successfully applied to the problem of sensitivity estimation of option prices as functions of the underlying stock price.

With the constant deepening of the railway reform in China, the competition between railway passenger transportation and other modes of passenger transportation has been getting fiercer. In this situation, the existing unitary and changeless fare structure gradually becomes the prevention of railway revenue increase and railway system development. This paper examines a new method for ticket fare optimization strategy based on the revenue management theory. On the premise that only one fare grade can be offered for each OD at the same time, this paper addresses the questions of how to determine the number of fare grades and the price of each fare grade. First, on the basis of piecewise pricing strategy, we build a ticket fare optimization model. After transforming this model to a convex program, we solve the original problem by finding the Kuhn-Tucker (K-T) point of the convex program. Finally, we verify the proposed method by real data of Beijing-Shanghai HSR line. The calculating result shows that our pricing strategy can not only increase the revenue, but also play a part in regulating the existing demand and stimulating potential demand.